b+15(b+2)*15(2b-9)=90

Solution for b+15(b+2)*15(2b-9)=90 equation:

Simplifying
b + 15(b + 2) * 15(2b + -9) = 90

Reorder the terms:
b + 15(2 + b) * 15(2b + -9) = 90

Reorder the terms:
b + 15(2 + b) * 15(-9 + 2b) = 90

Reorder the terms for easier multiplication:
b + 15 * 15(2 + b)(-9 + 2b) = 90

Multiply 15 * 15
b + 225(2 + b)(-9 + 2b) = 90

Multiply (2 + b) * (-9 + 2b)
b + 225(2(-9 + 2b) + b(-9 + 2b)) = 90
b + 225((-9 * 2 + 2b * 2) + b(-9 + 2b)) = 90
b + 225((-18 + 4b) + b(-9 + 2b)) = 90
b + 225(-18 + 4b + (-9 * b + 2b * b)) = 90
b + 225(-18 + 4b + (-9b + 2b2)) = 90

Combine like terms: 4b + -9b = -5b
b + 225(-18 + -5b + 2b2) = 90
b + (-18 * 225 + -5b * 225 + 2b2 * 225) = 90
b + (-4050 + -1125b + 450b2) = 90

Reorder the terms:
-4050 + b + -1125b + 450b2 = 90

Combine like terms: b + -1125b = -1124b
-4050 + -1124b + 450b2 = 90

Solving
-4050 + -1124b + 450b2 = 90

Solving for variable 'b'.

Reorder the terms:
-4050 + -90 + -1124b + 450b2 = 90 + -90

Combine like terms: -4050 + -90 = -4140
-4140 + -1124b + 450b2 = 90 + -90

Combine like terms: 90 + -90 = 0
-4140 + -1124b + 450b2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-2070 + -562b + 225b2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-2070 + -562b + 225b2)' equal to zero and attempt to solve:

Simplifying
-2070 + -562b + 225b2 = 0

Solving
-2070 + -562b + 225b2 = 0

Begin completing the square.  Divide all terms by
225 the coefficient of the squared term: 

Divide each side by '225'.
-9.2 + -2.497777778b + b2 = 0

Move the constant term to the right:

Add '9.2' to each side of the equation.
-9.2 + -2.497777778b + 9.2 + b2 = 0 + 9.2

Reorder the terms:
-9.2 + 9.2 + -2.497777778b + b2 = 0 + 9.2

Combine like terms: -9.2 + 9.2 = 0.0
0.0 + -2.497777778b + b2 = 0 + 9.2
-2.497777778b + b2 = 0 + 9.2

Combine like terms: 0 + 9.2 = 9.2
-2.497777778b + b2 = 9.2

The b term is -2.497777778b.  Take half its coefficient (-1.248888889).
Square it (1.559723457) and add it to both sides.

Add '1.559723457' to each side of the equation.
-2.497777778b + 1.559723457 + b2 = 9.2 + 1.559723457

Reorder the terms:
1.559723457 + -2.497777778b + b2 = 9.2 + 1.559723457

Combine like terms: 9.2 + 1.559723457 = 10.759723457
1.559723457 + -2.497777778b + b2 = 10.759723457

Factor a perfect square on the left side:
(b + -1.248888889)(b + -1.248888889) = 10.759723457

Calculate the square root of the right side: 3.28020174

Break this problem into two subproblems by setting 
(b + -1.248888889) equal to 3.28020174 and -3.28020174.

Subproblem 1
b + -1.248888889 = 3.28020174

Simplifying
b + -1.248888889 = 3.28020174

Reorder the terms:
-1.248888889 + b = 3.28020174

Solving
-1.248888889 + b = 3.28020174

Solving for variable 'b'.

Move all terms containing b to the left, all other terms to the right.

Add '1.248888889' to each side of the equation.
-1.248888889 + 1.248888889 + b = 3.28020174 + 1.248888889

Combine like terms: -1.248888889 + 1.248888889 = 0.000000000
0.000000000 + b = 3.28020174 + 1.248888889
b = 3.28020174 + 1.248888889

Combine like terms: 3.28020174 + 1.248888889 = 4.529090629
b = 4.529090629

Simplifying
b = 4.529090629

Subproblem 2
b + -1.248888889 = -3.28020174

Simplifying
b + -1.248888889 = -3.28020174

Reorder the terms:
-1.248888889 + b = -3.28020174

Solving
-1.248888889 + b = -3.28020174

Solving for variable 'b'.

Move all terms containing b to the left, all other terms to the right.

Add '1.248888889' to each side of the equation.
-1.248888889 + 1.248888889 + b = -3.28020174 + 1.248888889

Combine like terms: -1.248888889 + 1.248888889 = 0.000000000
0.000000000 + b = -3.28020174 + 1.248888889
b = -3.28020174 + 1.248888889

Combine like terms: -3.28020174 + 1.248888889 = -2.031312851
b = -2.031312851

Simplifying
b = -2.031312851

Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {4.529090629, -2.031312851}
Solution
b = {4.529090629, -2.031312851}